Subscribing Manually

Copy the web address (URL) for the podcast feed you are interested from the podcast's website. Then in iTunes, from the top menus select Advanced -> Subscribe to Podcast. You will get a dialogue box where you can enter the URL you just copied.

Once you subscribe to the podcast, it will show up in your list of podcasts available in the Podcasts directory. The latest episode of the podcast should also begin downloading.

TIP: You can have iTunes automatically download all episodes for your podcasts by going to iTunes -> Preferences -> Podcasts and selecting Download All for the When New Episodes Are Available option.

Subscribing via the iTunes Music Store

Some podcast sites will provide you with a link you can click on to subscribe to their podcast via iTunes. When you click on the link, it will take you to their podcast's homepage in the iTunes Music Store, which will allow you to review the podcast's description, preview episodes, and verify if there is a fee (it's rare, but out there) before you subscribe.

When you are ready, click on the Subscribe button. The podcast will now show up in your list of podcasts available in the Podcasts Directory. The latest episode of the podcast should also begin downloading.